Swimming pools are conventionally heated by introducing hot water (110xc2x0 to 120xc2x0 F.) into the pool at a velocity not exceeding 12 ft/sec to avoid large pressure losses. The heating system (very much like a water heater) heats a copper coil inside which the water travels, wasting 80 to 90% of the heat. Enormous losses occur when trying to heat a standard swimming pool of 22 ft.xc3x9715 ftxc3x975 ft with 12,000 gal of water. During the heating process, heat is lost by evaporation from the pool surface to the environment at a rate proportional to the difference in temperature between the pool water and the atmosphere. The slower the water is heated, the greater the heat loss.
Heat transfer velocity is a function of             ⅆ      E              ⅆ      t        =      f    ⁡          (                        Δ          ⁢                      xe2x80x83                    ⁢                      V            2                          ,        φ        ,                  Δ          ⁢                      xe2x80x83                    ⁢          T                    )      
xcex94V2=Relative Velocity of the two elements
xcfx86=Flow rate of Heating Media
xcex94T=Difference in temperature of the two elements
If superheated gas is introduced into the water at a very high velocity using a jet reactor pump, maximum heat transfer per unit time is possible since:
a) The gas can be introduced at a near sonic velocity (several orders of magnitude over 12 ft/sec)
b) Gas (air) can be heated to any temperature without the concern of vapor locking the system (for fabrication simplicity and safety, I recommend approximately 360xc2x0 F. to 400xc2x0 F.).
c) The gas/liquid flow efficiency of a jet reactor pump is well above 50% (volume to volume) which is several times a liquid/liquid pump. A liquid/liquid pump could be used, except that it has a maximum temperature limitation that gas/liquid does not.
d) A 4xe2x80x3 diameter pipe jet reactor pump could circulate all the water in a 12,000-gallon pool in two hours or less vs. 12 to 24 hours for present hot water systems.
e) The losses of heating the water pipe (convectionxe2x80x94conduction), to heat the water (convection) and to inject in the pool water (conduction) is eliminated by simply heating the air inserted in the jet reactor that pumps the water as it is being heated.
f) As the water heats up, xcex94T diminishes, reducing the heat transfer velocity (in the present systems)
Twater≈12020  Tstart pool≈50xc2x0 F. Tfinish pool=70xc2x0 F.
xcex94Tstart=120xe2x88x9250=70xc2x0 F.
xcex94Tfinish=120xe2x88x9270=50xc2x0 F.
with gas @ 360xc2x0 F.
xcex94Tstart=360xe2x88x9250=310xc2x0 F.
xcex94Tfinish=360xe2x88x9270=290xc2x0 F.
This shows almost five times better temperature differential transfer rate at the start of heating, and almost six times better differential at the end of the cycle.
Preferably a compressor is used that is capable of delivering 50 to 75 ft3/min. of air @ 50 to 60 psig of pressure (this pressure assures gas sonic velocity in the jet reactor nozzles). Before inserting the air in the jet pump, a heater increases the air temperature to 360xc2x0 F. to 400xc2x0 F. The higher the gas temperature, the higher the thermodynamic efficiency of the heating cycle. The gas volume expansion at constant pressure will be:                     V        2                    V        1              =                                        T            2                                T            1                          ⁢                  T          2                ⁢                  xe2x80x83                ⁢        and        ⁢                  xe2x80x83                ⁢                  T          1                    =              Absolute        ⁢                  xe2x80x83                ⁢        temperature                                50        ⁢                  xe2x80x83                ⁢                              ft            3                    /          min                xc3x97        860            520        ≅                  83        ⁢                  xe2x80x83                ⁢                  ft          3                    min      
This represents a water flow of approximately 42 ft3/min of water from the jet reactor pump or over 300gal/min which would allow the recirculation of a 12,000 gal pool in less than 40 minutes, unheard of in any water heater/water pump system.